www.jeebooks.

in
5
P-54 Physics

Work, Energy and

Power
1 3
TOPIC 1 Work (a) 2J (b)J (c) 1J (d) J
2 2
4. A block of mass m is kept on a platform which starts
1. A person pushes a box on a rough horizontal platform from rest with constant acceleration g/2 upward, as
surface. He applies a force of 200 N over a distance of shown in fig. work done by normal reaction on block in
15 m. Thereafter, he gets progressively tired and his applied time t is: [10 Jan. 2019 I]
force reduces linearly with distance to 100 N. The total
distance through which the box has been moved is 30 m.
What is the work done by the person during the total
movement of the box ? [4 Sep. 2020 (II)]
(a) 3280 J (b) 2780 J m g2 t 2 m g2 t2
(a) - (b)
(c) 5690 J (d) 5250 J 8 8
2. B 3m g 2 t 2
C (c) 0 (d)
8
A q 5. A body of mass starts moving from rest along x-axis so
A small block starts slipping down from a point B on an that its velocity varies as v = a s where a is a constant s
inclined plane AB, which is making an angle q with the and is the distance covered by the body. The total work
horizontal section BC is smooth and the remaining section done by all the forces acting on the body in the first second
CA is rough with a coefficient of friction m. It is found that after the start of the motion is: [Online April 16, 2018]
the block comes to rest as it reaches the bottom (point A) 1 4 2
(a) ma t (b) 4ma 4 t 2
of the inclined plane. If BC = 2AC, the coefficient of friction 8
is given by m = k tanq. The value of k is _________. 1
(c) 8ma 4 t 2 (d) ma 4 t 2
4
[NA 2 Sep. 2020 (I)] 6. When a rubber-band is stretched by a distance x, it exerts
r restoring force of magnitude F = ax + bx2 where a and b are
3. Consider a force F = - xiˆ + yjˆ . The work done by this
constants. The work done in stretching the unstretched
force in moving a particle from point A(1, 0) to B(0, 1) rubber-band by L is: [2014]

( )
along the line segment is: (all quantities are in SI units) 1
(a) aL2 + bL3 (b) aL2 + bL3
[9 Jan. 2020 I] 2

aL2 bL3 1 æ aL2 bL3 ö

(c) + (d) 2 çç 2 + 3 ÷÷
2 3 è ø
7. A uniform chain of length 2 m is kept on a table such that
a length of 60 cm hangs freely from the edge of the table.
The total mass of the chain is 4 kg. What is the work done
in pulling the entire chain on the table ? [2004]
(a) 12 J (b) 3.6 J (c) 7.2 J (d) 1200 J
 www.jeebooks.in
Work, Energy & Power P-55
r r r r
8. A force F = (5i + 3 j + 2k ) N is applied over a particle 14. A spring whose unstretched length is l has a force
which displaces it from its origin to the point constant k. The spring is cut into two pieces of
r r r unstretched lengths 11 and l2 where, l1 = nl2 and n is an
r = (2i - j )m. The work done on the particle in joules is
integer. The ratio k 1/k 2 of the corresponding force
[2004] constants, k1 and k2 will be: [12 April 2019 II]
(a) +10 (b) +7 (c) –7 (d) +13 1 1
9. A spring of spring constant 5 × 103 N/m is stretched initially (a) n (b) 2 (c) (d) n 2
n n
by 5cm from the unstretched position. Then the work 15. A body of mass 1 kg falls freely from a height of 100m, on
required to stretch it further by another 5 cm is [2003] a platform of mass 3 kg which is mounted on a spring
(a) 12.50 N-m (b) 18.75 N-m having spring constant k = 1.25 × 106 N/m. The body sticks
(c) 25.00 N-m (d) 6.25 N-m
to the platform and the spring’s maximum compression is
10. A spring of force constant 800 N/m has an extension of 5 cm.
The work done in extending it from 5 cm to 15 cm is found to be x. Given that g = 10 ms–2, the value of x will be
[2002] close to : [11 April 2019 I]
(a) 16 J (b) 8 J (c) 32 J (d) 24 J (a) 40 cm (b) 4 cm (c) 80 cm (d) 8 cm
16. A uniform cable of mass ‘M’ and length ‘L’ is placed on a
th
TOPIC 2 Energy æ 1ö
horizontal surface such that its ç ÷ part is hanging
è nø
11. A cricket ball of mass 0.15 kg is thrown vertically up by a below the edge of the surface. To lift the hanging part of
bowling machine so that it rises to a maximum height of 20 the cable upto the surface, the work done should be:
m after leaving the machine. If the part pushing the ball [9 April 2019 I]
applies a constant force F on the ball and moves MgL MgL 2MgL
horizontally a distance of 0.2 m while launching the ball, (a) 2 (b) 2 (c) (d) nMgL
2n n n2
the value of F (in N) is (g = 10 ms–2) __________.
17. A wedge of mass M = 4m lies on a frictionless plane. A
[NA 3 Sep. 2020 (I)] particle of mass m approaches the wedge with speed v.
12. A particle (m = l kg) slides down a frictionless track There is no friction between the particle and the plane
(AOC) starting from rest at a point A (height 2 m). After or between the particle and the wedge. The maximum
reaching C, the particle continues to move freely in air height climbed by the particle on the wedge is given by:
as a projectile. When it reaching its highest point P [9 April 2019 II]
(height 1 m), the kinetic energy of the particle (in J) is: v2 2v 2
(Figure drawn is schematic and not to scale; take g = 10 (a) (b)
g 7g
ms–2) ¾¾¾ . [NA 7 Jan. 2020 I]
2v 2 v2
Height (c) (d)
A
P 5g 2g
18. A particle moves in one dimension from rest under the
influence of a force that varies with the distance travelled
2m C
by the particle as shown in the figure. The kinetic energy
of the particle after it has travelled 3 m is :
[8 April 2019 I]
O

13. A particle moves in one dimension from rest under the

influence of a force that varies with the distance travelled
by the particle as shown in the figure. The kinetic energy
of the particle after it has travelled 3 m is :
[7 Jan. 2020 II]

(a) 4 J (b) 2.5 J

(c) 6.5 J (d) 5 J
19. A particle which is experiencing a force, given by
r r r r r
F = 3i - 12 j, undergoes a displacement of d = 4i. If
the particle had a kinetic energy of 3 J at the beginning
of the displacement, what is its kinetic energy at the end
(a) 4 J (b) 2.5 J of the displacement? [10 Jan. 2019 II]
(c) 6.5 J (d) 5 J (a) 9 J (b) 12 J
(c) 10 J (d) 15 J
 www.jeebooks.in
P-56 Physics

20. A block of mass m, lying on a smooth horizontal surface, v (m/s)

-1
50 ms
is attached to a spring (of negligible mass) of spring
constant k. The other end of the spring is fixed, as shown
in the figure. The block is initally at rest in its equilibrium
position. If now the block is pulled with a constant force
F, the maximum speed of the block is: [9 Jan. 2019 I]
(0,0) 10s t(s)

m (a) – 9300 J (b) 12000 J

F
(c) –4500 J (d) –12000 J
2F F pF F 28. A point particle of mass m, moves long the uniformly
(a) (b) (c) (d) rough track PQR as shown in the figure. The coefficient
mk p mk mk mk of friction, between the particle and the rough track
21. A force acts on a 2 kg object so that its position is given equals m. The particle is released, from rest from the
as a function of time as x = 3t2 + 5. What is the work
done by this force in first 5 seconds? point P and it comes to rest at a point R. The energies,
[9 Jan. 2019 II] lost by the ball, over the parts, PQ and QR, of the track,
(a) 850 J (b) 950 J (c) 875 J (d) 900 J are equal to each other, and no energy is lost when particle
22. A particle is moving in a circular path of radius a under the changes direction from PQ to QR.
k The value of the coefficient of friction m and the distance
action of an attractive potential U = - . Its total energy is: x (= QR), are, respectively close to : [2016]
2r 2
[2018] P
k k
(a) - (b) h=2m
4a 2 2a 2
30° R
3 k
(c) zero (d) - 2 Horizontal Q
2a Surface
23. Two particles of the same mass m are moving in circular (a) 0.29 and 3.5 m (b) 0.29 and 6.5 m
-16 3 (c) 0.2 and 6.5 m (d) 0.2 and 3.5 m
orbits because of force, given by F(r) = -r
29. A person trying to lose weight by burning fat lifts a mass
r
The first particle is at a distance r = 1, and the second, at of 10 kg upto a height of 1 m 1000 times. Assume that the
r = 4. The best estimate for the ratio of kinetic energies potential energy lost each time he lowers the mass is
of the first and the second particle is closest to dissipated. How much fat will he use up considering the
[Online April 16, 2018] work done only when the weight is lifted up? Fat supplies
(a) 10–1 (b) 6 × 10–2 (c) 6 × 102 (d) 3 × 10–3 3.8 × 107 J of energy per kg which is converted to
24. A body of mass m = 10–2 kg is moving in a medium and mechanical energy with a 20% efficiency rate. Take g = 9.8
experiences a frictional force F = –kv2. Its intial speed is v0 = ms–2 : [2016]
1 2 (a) 9.89 × 10–3 kg (b) 12.89 × 10–3 kg
10 ms–1. If, after 10 s, its energy is mv0 , the value of k will
8 (c) 2.45 × 10–3 kg (d) 6.45 × 10–3 kg
be: [2017] 30. A particle is moving in a circle of radius r under the action
(a) 10–4 kg m–1 (b) 10–1 kg m–1 s–1 of a force F = ar2 which is directed towards centre of the
(c) 10–3 kg m–1 (d) 10–3 kg s–1 circle. Total mechanical energy (kinetic energy + potential
25. An object is dropped from a height h from the ground. energy) of the particle is (take potential energy = 0 for r = 0) :
Every time it hits the ground it looses 50% of its kinetic [Online April 11, 2015]
energy. The total distance covered as t ® ¥ is
1 3 5 3 4 3
[Online April 8, 2017] (a) ar (b) ar (c) αr (d) ar3
2 6 3
5 8 31. A block of mass m = 0.1 kg is connected to a spring of
(a) 3h (b) ¥ (c) h (d) h
3 3 unknown spring constant k. It is compressed to a distance
x from its equilibrium position and released from rest. After
26. A time dependent force F = 6t acts on a particle of mass
1 kg. If the particle starts from rest, the work done by the approaching half the distance æç x ö÷ from equilibrium
force during the first 1 second will be [2017] è 2ø
(a) 9 J (b) 18 J (c) 4.5 J (d) 22 J position, it hits another block and comes to rest
momentarily, while the other block moves with a velocity
27. Velocity–time graph for a body of mass 10 kg is shown in 3 ms–1.
figure. Work–done on the body in first two seconds of The total initial energy of the spring is :
the motion is : [Online April 10, 2016] [Online April 10, 2015]
 www.jeebooks.in
Work, Energy & Power P-57

(a) 0.3 J (b) 0.6 J (a) constant (b) t

(c) 0.8 J (d) 1.5 J
1
th (c) (d) t
æ1ö t
32. A bullet looses ç ÷ of its velocity passing through
ènø 38. The potential energy function for the force between two
one plank. The number of such planks that are required
to stop the bullet can be: [Online April 19, 2014] atoms in a diatomic molecule is approximately given by
a b
n2 2n 2 U(x) = 12 - 6 , where a and b are constants and x is
(a) (b) (c) infinite (d) n x x
2n - 1 n -1
the distance between the atoms. If the dissociation energy
33. A spring of unstretched length l has a mass m with one of the molecule is
end fixed to a rigid support. Assuming spring to be made
of a uniform wire, the kinetic energy possessed by it if its D = éëU ( x = ¥) - U at equilibrium ùû , D is [2010]
free end is pulled with uniform velocity v is:
b2 b2 b2 b2
[Online April 12, 2014] (a) (b) (c) (d)
2a 12a 4a 6a
1 1 2 1 39. An athlete in the olympic games covers a distance of 100
(a) mv 2 (b) mv2 (c) mv (d) mv 2
2 3 6 m in 10 s. His kinetic energy can be estimated to be in the
range [2008]
34. Two springs of force constants 300 N/m 5 5
(Spring A) and 400 N/m (Spring B) are joined together in (a) 200 J - 500 J (b) 2 × 10 J - 3 × 10 J
series. The combination is compressed by 8.75 cm. The (c) 20, 000 J - 50,000 J (d) 2,000 J - 5, 000 J
E E 40. A 2 kg block slides on a horizontal floor with a speed of 4m/
ratio of energy stored in A and B is A . Then A is s. It strikes a uncompressed spring, and compresses it till
EB EB
equal the block is motionless. The kinetic friction force is 15N and
to : [Online April 9, 2013] spring constant is 10,000 N/m. The spring compresses by
[2007]
4 16 3 9 (a) 8.5 cm (b) 5.5 cm
(a) (b) (c) (d)
3 9 4 16 (c) 2.5 cm (d) 11.0 cm
r 41. A particle is projected at 60o to the horizontal with a kinetic
35. The force F = Fiˆ on a particle of mass 2 kg, moving along
energy K. The kinetic energy at the highest point is
the x-axis is given in the figure as a function of its position
x. The particle is moving with a velocity of 5 m/s along the (a) K /2 (b) K [2007]
x-axis at x = 0. What is the kinetic energy of the particle at (c) Zero (d) K /4
x = 8 m? [Online May 26, 2012] 42. A particle of mass 100g is thrown vertically upwards with
a speed of 5 m/s. The work done by the force of gravity
3 during the time the particle goes up is [2006]
(a) –0.5 J (b) –1.25 J
2
(c) 1.25 J (d) 0.5 J
1
43. The potential energy of a 1 kg particle free to move along
F (in N)

0 x (in m) æ x 4 x2 ö
the x-axis is given by V ( x) = ç - ÷ J.
–1
è 4 2ø
–2 The total mechanical energy of the particle is 2 J. Then,
0 1 2 3 4 5 6 78 the maximum speed (in m/s) is [2006]
(a) 34 J (b) 34.5 J (c) 4.5 J (d) 29.4 J 3 1
36. A particle gets displaced by (a) (b) 2 (c) (d) 2
2 2
( )
D r = 2iˆ + 3 ˆj + 4kˆ m under the action of a force 44. A mass of M kg is suspended by a weightless string. The
r
( )
F = 7iˆ + 4 ˆj + 3kˆ . The change in its kinetic energy is
horizontal force that is required to displace it until the
string makes an angle of 45° with the initial vertical
[Online May 7, 2012] direction is [2006]
(a) 38 J (b) 70 J (c) 52.5 J (d) 126 J
(a) Mg ( 2 + 1) (b) Mg 2
37. At time t = 0 a particle starts moving along the x-axis. If
Mg
its kinetic energy increases uniformly with time ‘t’, the (c) (d) Mg ( 2 - 1)
net force acting on it must be proportional to [2011 RS] 2
 www.jeebooks.in
P-58 Physics

45. A spherical ball of mass 20 kg is stationary at the top of 52. A 60 HP electric motor lifts an elevator having a
a hill of height 100 m. It rolls down a smooth surface to maximum total load capacity of 2000 kg. If the frictional
the ground, then climbs up another hill of height 30 m and force on the elevator is 4000 N, the speed of the elevator
finally rolls down to a horizontal base at a height of 20 m at full load is close to: (1 HP = 746 W, g = 10 ms–2)
above the ground. The velocity attained by the ball is [7 Jan. 2020 I]
[2005] (a) 1.7 ms–1 (b) 1.9 ms–1
(a) 20 m/s (b) 40 m/s (c) 1.5 ms–1 (d) 2.0 ms–1
(c) 10 30 m/s (d) 10 m/s 53. A particle of mass M is moving in a circle of fixed radius
R in such a way that its centripetal acceleration at time t
46. A particle moves in a straight line with retardation is given by n2 R t2 where n is a constant. The power
proportional to its displacement. Its loss of kinetic energy delivered to the particle by the force acting on it, is :
for any displacement x is proportional to [2004] [Online April 10, 2016]
(a) x (b) e x (c) x2 (d) loge x
47. A particle is acted upon by a force of constant magnitude 1
(a) M n2 R2t2 (b) M n2R2t
which is always perpendicular to the velocity of the particle, 2
the motion of the particles takes place in a plane. It follows (c) M n R2t2 (d) M n R2t
that [2004] 54. A car of weight W is on an inclined road that rises by 100
(a) its kinetic energy is constant m over a distance of 1 Km and applies a constant frictional
(b) its acceleration is constant W
(c) its velocity is constant force on the car. While moving uphill on the road at
20
(d) it moves in a straight line a speed of 10 ms–1, the car needs power P. If it needs
48. A wire suspended vertically from one of its ends is
P
stretched by attaching a weight of 200N to the lower end. power while moving downhill at speed v then value of
The weight stretches the wire by 1 mm. Then the elastic 2
v is: [Online April 9, 2016]
energy stored in the wire is [2003]
(a) 20 ms–1 (b) 5 ms–1 (c) 15 ms–1 (d) 10 ms–1
(a) 0.2 J (b) 10 J (c) 20 J (d) 0.1 J
55. A wind-powered generator converts wind energy into electrical
49. A ball whose kinetic energy is E, is projected at an angle of energy. Assume that the generator converts a fixed fraction
45° to the horizontal. The kinetic energy of the ball at the of the wind energy intercepted by its blades into electrical
highest point of its flight will be [2002] energy. For wind speed n, the electrical power output will be
(a) E (b) E / 2 (c) E/2 (d) zero most likely proportional to
[Online April 25, 2013]
(a) n 4 (b) n 2 (c) n (d) n
TOPIC 3 Power 56. A 70 kg man leaps vertically into the air from a crouching
position. To take the leap the man pushes the ground with
50. A body of mass 2 kg is driven by an engine delivering a a constant force F to raise himself. The center of gravity
constant power of 1 J/s. The body starts from rest and rises by 0.5 m before he leaps. After the leap the c.g. rises
moves in a straight line. After 9 seconds, the body has by another 1 m. The maximum power delivered by the
moved a distance (in m) ________. [5 Sep. 2020 (II)] muscles is : (Take g = 10 ms–2) [Online April 23, 2013]
51. A particle is moving unidirectionally on a horizontal plane (a) 6.26 × 103 Watts at the start
under the action of a constant power supplying energy
source. The displacement (s) - time (t) graph that describes (b) 6.26 × 103 Watts at take off
the motion of the particle is (graphs are drawn schematically (c) 6.26 × 104 Watts at the start
and are not to scale) : [3 Sep. 2020 (II)] (d) 6.26 × 104 Watts at take off
S S 57. A body of mass ‘m’, accelerates uniformly from rest to ‘v1’
in time ‘t1’. The instantaneous power delivered to the body
as a function of time ‘t’ is [2004]
mv1t 2 mv12t
(a) (b) (a) (b)
t1 t12
t t mv1t mv12t
S S (c) t (d)
1 t1
58. A body is moved along a straight line by a machine
delivering a constant power. The distance moved by the
(c) (d) body in time ‘t’ is proportional to [2003]
t t (a) t3/4 (b) t3/2 (c) t1/4 (d) t1/2
 www.jeebooks.in
Work, Energy & Power P-59

64. A particle of mass m is moving along the x-axis with initial

TOPIC 4 Collisions velocity uiˆ. It collides elastically with a particle of mass
10 m at rest and then moves with half its initial kinetic
59. Two bodies of the same mass are moving with the same energy (see figure). If sin q1 = n sin q2 , then value of n
speed, but in different directions in a plane. They have a is ___________. [NA 2 Sep. 2020 (II)]
completely inelastic collision and move together m
thereafter with a final speed which is half of their initial q1
speed. The angle between the initial velocities of the m 10 m q2
ui$
two bodies (in degree) is ______.[NA 6 Sep. 2020 (I)]
10 m
60. Particle A of mass m moving with velocity ( 3$i + $j ) ms-1
1
65. Two particles of equal mass m have respective initial
collides with another particle B of mass m2 which is at rest æ iˆ + ˆj ö
r r velocities uiˆ and u ç 2 ÷ . They collide completely
initially. Let V1 and V2 be the velocities of particles A and è ø
B after collision respectively. If m1 = 2m2 and after collision inelastically. The energy lost in the process is: [9 Jan. 2020 I]
r r r 1 1
V1 = ($i + 3 $j ) ms -1 , the angle between V1 and V2 is : (a) mu2 (b) mu2
3 8
[6 Sep. 2020 (II)]
3 2
(a) 15º (b) 60º (c) mu2 (d) mu2
4 3
(c) – 45º (d) 105º 66. A body A, of mass m = 0.1 kg has an initial velocity of 3 iˆ ms–1.
61. Blocks of masses m, 2m, 4m and 8m are arranged in a line on It collides elastically with another body, B of the same
a frictionless floor. Another block of mass m, moving with
speed v along the same line (see figure) collides with mass mass which has an initial velocity of 5 ĵ ms–1. After
r
m in perfectly inelastic manner. All the subsequent collisions
are also perfectly inelastic. By the time the last block of
(
collision, A moves with a velocity v = 4 iˆ + ˆj . The )
mass 8m starts moving the total energy loss is p% of the x
energy of B after collision is written as
J. The value of
original energy. Value of ‘p’ is close to : 10
[4 Sep. 2020 (I)] x is _______. [NA 8 Jan. 2020 I]
67. A particle of mass m is dropped from a height h above the
v
ground. At the same time another particle of the same
mass is thrown vertically upwards from the ground with a
m m 2m 4m 8m speed of 2 gh . If they collide head-on completely
(a) 77 (b) 94 inelastically, the time taken for the combined mass to reach
(c) 37 (d) 87
62. A block of mass 1.9 kg is at rest at the edge of a table, of h
height 1 m. A bullet of mass 0.1 kg collides with the block the ground, in units of is: [8 Jan. 2020 II]
g
and sticks to it. If the velocity of the bullet is 20 m/s in
the horizontal direction just before the collision then the 1 3
(a) (b)
kinetic energy just before the combined system strikes 2 4
the floor, is [Take g = 10 m/s2 . Assume there is no 1 3
rotational motion and losss of energy after the collision (c) (d)
is negligiable.] 2 2
68. A man (mass = 50 kg) and his son (mass = 20 kg) are
[3 Sep. 2020 (II)]
standing on a frictionless surface facing each other. The
(a) 20 J (b) 21 J (c) 19 J (d) 23 J
man pushes his son so that he starts moving at a speed of
63. A particle of mass m with an initial velocity u iˆ collides 0.70 ms–1 with respect to the man. The speed of the man
perfectly elastically with a mass 3 m at rest. It moves with respect to the surface is : [12 April 2019 I]
with a velocity v ˆj after collision, then, v is given by : (a) 0.28 ms–1 (b) 0.20 ms–1
[2 Sep. 2020 (I)] (c) 0.47 ms–1 (d) 0.14 ms–1
2 u 69. Two particles, of masses M and 2M, moving, as shown,
(a) v = u (b) v =
3 3 with speeds of 10 m/s and 5 m/s, collide elastically at the
u 1 origin. After the collision, they move along the indicated
(c) v = (d) v = u directions with speeds v1 and v2, respectively. The values
2 6
of v1 and v2 are nearly : [10 April 2019 I]
 www.jeebooks.in
P-60 Physics

5
C, also perfectly inelastically th of the initial kinetic
6
energy is lost in whole process. What is value of M/m?
[9 Jan. 2019 I]
A B C
m m M

(a) 6.5 m/s and 6.3 m/s (b) 3.2 m/s and 6.3 m/s (a) 5 (b) 2 (c) 4 (d) 3
(c) 6.5 m/s and 3.2 m/s (d) 3.2 m/s and 12.6 m/s 76. In a collinear collision, a particle with an initial speed n0
70. A body of mass 2 kg makes an elastic collision with a strikes a stationary particle of the same mass. If the final
second body at rest and continues to move in the original total kinetic energy is 50% greater than the original
direction but with one fourth of its original speed. What kinetic energy, the magnitude of the relative velocity
is the mass of the second body? [9 April 2019 I] between the two particles, after collision, is: [2018]
(a) 1.0 kg (b) 1.5 kg (c) 1.8 kg (d) 1.2 kg n0
n0 n0
71. A particle of mass ‘m’ is moving with speed ‘2v’ and (a) (b) 2n0 (c) (d)
collides with a mass ‘2m’ moving with speed ‘v’ in the 4 2 2
same direction. After collision, the first mass is stopped 77. The mass of a hydrogen molecule is 3.32×10–27 kg. If 1023
completely while the second one splits into two particles hydrogen molecules strike, per second, a fixed wall of area
each of mass ‘m’, which move at angle 45° with respect to 2 cm2 at an angle of 45° to the normal, and rebound
the original direction. [9 April 2019 II] elastically with a speed of 103 m/s, then the pressure on
The speed of each of the moving particle will be: the wall is nearly: [2018]
(a) 2.35 × 103 N/m2 (b) 4.70 × 103 N/m2
(a) 2 v (b) 2 2 v
(c) 2.35 × 102 N/m2 (d) 4.70 × 102 N/m2
(c) v / (2 2) (d) v/ 2 78. It is found that if a neutron suffers an elastic collinear
72. A body of mass m1 moving with an unknown velocity of collision with deuterium at rest, fractional loss of its energy
is pd; while for its similar collision with carbon nucleus at
v1 iˆ , undergoes a collinear collision with a body of mass
rest, fractional loss of energy is Pc. The values of Pd and
m2 moving with a velocity v2 iˆ . After collision, m1 and m2 Pc are respectively: [2018]
move with velocities of v3 iˆ and v4 iˆ , respectively.. (a) ( ×89, ×28) (b) ( ×28, ×89 ) (c) (0, 0) (d) (0, 1)
If m2 = 0.5 m1 and v3 = 0.5 v1, then v1 is : [8 April 2019 II] 79. A proton of mass m collides elastically with a particle of
v v unknown mass at rest. After the collision, the proton and
(a) v4 – 2 (b) v4 – v2 (c) v4 – 2 (d) v4 + v2 the unknown particle are seen moving at an angle of 90°
2 4
73. An alpha-particle of mass m suffers 1-dimensional elastic with respect to each other. The mass of unknown particle
collision with a nucleus at rest of unknown mass. It is is: [Online April 15, 2018]
scattered directly backwards losing, 64% of its initial m m
kinetic energy. The mass of the nucleus is : (a) (b) (c) 2m (d) m
3 2
[12 Jan. 2019 II] 80. Two particles A and B of equal mass M are moving with
(a) 2 m (b) 3.5 m (c) 1.5 m (d) 4 m the same speed v as shown in the figure. They collide
74. A piece of wood of mass 0.03 kg is dropped from the completely inelastically and move as a single particle C.
top of a 100 m height building. At the same time, a bullet The angle q that the path of C makes with the X-axis is
of mass 0.02 kg is fired vertically upward, with a velocity given by: [Online April 9, 2017]
100 ms–1, from the ground. The bullet gets embedded in
the wood. Then the maximum height to which the 3+ 2 Y
(a) tanq =
combined system reaches above the top of the building 1- 2
before falling below is: (g = 10 ms–2) [10 Jan. 2019 I]
C
(a) 20 m (b) 30 m (c) 40 m (d) 10 m 3- 2
(b) tanq =
75. There block A, B and C are lying on a smooth horizontal 1- 2 q
X
surface, as shown in the figure. A and B have equal
1- 2 A 45°
masses, m while C has mass M. Block A is given an inital (c) tanq = 30°
2(1 + 3) B
speed v towards B due to which it collides with B
perfectly inelastically. The combined mass collides with 1- 3
(d) tanq =
1+ 2
 www.jeebooks.in
Work, Energy & Power P-61

81. A neutron moving with a speed 'v' makes a head on 86. A projectile of mass M is fired so that the horizontal
collision with a stationary hydrogen atom in ground state. range is 4 km. At the highest point the projectile explodes
The minimum kinetic energy of the neutron for which in two parts of masses M/4 and 3M/4 respectively and
inelastic collision will take place is : the heavier part starts falling down vertically with zero
[Online April 10, 2016] initial speed. The horizontal range (distance from point
(a) 20.4 eV (b) 10.2 eV (c) 12.1 eV (d) 16.8 eV of firing) of the lighter part is :
82. A particle of mass m moving in the x direction with speed [Online April 23, 2013]
2v is hit by another particle of mass 2m moving in the y (a) 16 km (b) 1 km (c) 10 km (d) 2 km
direction with speed v. If the collision is perfectly inelastic, 87. A moving particle of mass m, makes a head on elastic
the percentage loss in the energy during the collision is collision with another particle of mass 2m, which is initially
close to : [2015] at rest. The percentage loss in energy of the colliding
(a) 56% (b) 62% (c) 44% (d) 50% particle on collision, is close to
83. A bullet of mass 4g is fired horizontally with a speed of [Online May 19, 2012]
300 m/s into 0.8 kg block of wood at rest on a table. If the (a) 33% (b) 67% (c) 90% (d) 10%
coefficient of friction between the block and the table is 88. Two bodies A and B of mass m and 2m respectively are
0.3, how far will the block slide approximately? placed on a smooth floor. They are connected by a spring
[Online April 12, 2014] of negligible mass. A third body C of mass m is placed
(a) 0.19 m (b) 0.379 m (c) 0.569 m (d) 0.758 m on the floor. The body C moves with a velocity v0 along
84. Three masses m, 2m and 3m are moving in x-y plane with the line joining A and B and collides elastically with A.
speed 3u, 2u and u respectively as shown in figure. The At a certain time after the collision it is found that the
three masses collide at the same point at P and stick instantaneous velocities of A and B are same and the
together. The velocity of resulting mass will be: compression of the spring is x0. The spring constant k
will be [Online May 12, 2012]
[Online April 12, 2014]
y v02 v0
(a) m (b) m 2 x
2m, 2u x02 0
2
v0 2 æ v0 ö
60° (c) 2m x (d) m
x 0 3 çè x0 ÷ø
m, 3u P 60°
89. A projectile moving vertically upwards with a velocity of
3m, u 200 ms–1 breaks into two equal parts at a height of 490 m.
One part starts moving vertically upwards with a velocity
(a)
u ˆ
12
(
i + 3jˆ ) (b)
u ˆ
12
(
i - 3jˆ ) of 400 ms–1. How much time it will take, after the break
up with the other part to hit the ground?
(c)
u ˆ
12
(
-i + 3jˆ ) (d)
u ˆ
12
(
-i - 3jˆ ) [Online May 12, 2012]

85. This question has statement I and statement II. Of the four (a) 2 10 s (b) 5 s
choices given after the statements, choose the one that
best describes the two statements. (c) 10 s (d) 10 s
Statement - I: Apoint particle of mass m moving with 90. Statement -1: Two particles moving in the same direction
speed u collides with stationary point particle of mass do not lose all their energy in a completely inelastic
M. If the maximum energy loss possible is given as collision.
æ1 ö Statement -2 : Principle of conservation of momentum
f ç mv2 ÷ then f = æç m ö÷ . holds true for all kinds of collisions. [2010]
è2 ø
èM + mø (a) Statement -1 is true, Statement -2 is true ; Statement
Statement - II: Maximum energy loss occurs when the -2 is the correct explanation of Statement -1.
particles get stuck together as a result of the collision. (b) Statement -1 is true, Statement -2 is true; Statement -2
[2013] is not the correct explanation of Statement -1
(a) Statement - I is true, Statment - II is true, Statement (c) Statement -1 is false, Statement -2 is true.
- II is the correct explanation of Statement - I. (d) Statement -1 is true, Statement -2 is false.
(b) Statement-I is true, Statment - II is true, Statement - 91. A block of mass 0.50 kg is moving with a speed of 2.00
II is not the correct explanation of Statement - II. ms–1 on a smooth surface. It strikes another mass of 1.00
(c) Statement - I is true, Statment - II is false. kg and then they move together as a single body. The
(d) Statement - I is false, Statment - II is true. energy loss during the collision is [2008]
(a) 0.16 J (b) 1.00 J (c) 0.67 J (d) 0.34 J
 www.jeebooks.in
P-62 Physics

(a) 0.16 J (b) 1.00 J (c) 0.67 J (d) 0.34 J

the l st mass moves with velocity
v
92. A bomb of mass 16kg at rest explodes into two pieces of in a direction
3
masses 4 kg and 12 kg. The velolcity of the 12 kg mass is perpendicular to the initial direction of motion. Find the
4 ms–1. The kinetic energy of the other mass is [2006]
speed of the 2 nd mass after collision. [2005]
(a) 144 J (b) 288 J (c) 192 J (d) 96 J
93. The block of mass M moving on the frictionless horizontal m m v
3
surface collides with the spring of spring constant k and A before Aafter
compresses it by length L. The maximum momentum of collision collision
the block after collision is [2005] v 2
(a) 3v (b) v (c) v
(d)
M 3 3
95. Consider the following two statements : [2003]
A. Linear momentum of a system of particles is zero
kL2 ML2 B. Kinetic energy of a system of particles is zero.
(a) (b) Mk L (c) (d) zero Then
2M k
(a) A does not imply B and B does not imply A
94. A mass ‘m’ moves with a velocity ‘v’ and collides
(b) A implies B but B does not imply A
inelastically with another identical mass. After collision
(c) A does not imply B but B implies A
(d) A implies B and B implies A